New book on volatility smile

There's a new book by Emanuel Derman, the famous quant guru. I'm still working thru the early chapters but already liking it very much. The book describes the bs model, explains the inaccuracies and attempts to provide workarounds. For those who enjoy things under the hood and don't mind options math, this is a good book to read.

Thanks for the heads up on this Kevin, just ordered my copy. Looks like it might be a good purchase for anyone just beginning their exploration of skew from the quantitative side - if it's what I expect, it could largely replace 10 older books, providing a faster and smoother learning curve for beginners.

Nam, I'm interested because I've never known an equity index trader that used SABR as a primary model (interest rates and fx yes, equity index no). Questions:

1.
The SABR models I'm (barely) familiar with only have 4 parameters to fit the model to the market's skew ... I believe it is a mathematical fact that equity index skews cannot be well-fitted with fewer than 5 parameters, and that's just the "meat" between, say, the 5 delta puts and calls - more parameters are needed to fit the far wings. In particular, butterfly pricing is going to be poor, in general, with any 4-parameter fit. Do you have a way around this, perhaps by using a modification with more degrees of freedom?

2.
Have you tested the skew dynamics of the SABR model? My understanding is that SABR is a pure "sticky delta" model, and these models perform poorly in replicating equity index call-side dynamics.

Very good questions. I just switched from using a naive regression model to SABR, so I'm still playing around to see if it works well.

1- My main concern right now is the model robustness, so I prefer a model with few parameters. Currently, in the SARB model I read the ATM vol directly from the market, set beta=1, so technically I only have 2 parameters (vol of vol and correlation). Also I'm mostly concerned with the center and right strikes of the BWB, for which SABR produced a reasonably good fit, and ignored the 5 delta puts and calls at the moment

2- It's sticky delta if you set beta=1. otherwise it's not. You can calibrate the beta to the market as well. Graeme West did a calibration to an equity index and found beta=0.7. Myself I prefer to use beta=1 (yes, sticky delta) then use a model to describe the dynamics of the backbone as a function of spot

Ok I get it, you are in exploratory mode and not concerned yet with nailing the whole skew. If you decide you like the SABR functional form and want to use it for the skew functional workhorse in your "real market" analytics engine then there are several generic things you can do to make this happen:
1.
Create a skew function with adequate degrees of freedom by using 2 independent SABR functions, one for put side and one for call side, and stitch them together at the money with a smooth transition function so the whole thing is continuously differentiable.
2.
Add simple second-order wing functions for far calls and far puts so the whole thing is at least once continuously differentiable.
3.
Make a 100% static version of #2, and make the U-dynamics more flexible by allowing for a combination of the dynamic and static versions.
4.
Add a more or less generic function for correcting the backbone behavior so the model has more flexibility to conform to the real market behavior.

My copy was delivered yesterday. Looking forward to digging in. Last book on the subject that I read was Taleb's Dynamic Hedging, and I was mildly unimpressed - mostly poor editing. Hope for better with Derman.

Steve and Kevin please come back with your impressions of the book after you have made at least one full reading. Thanks! ​

I agree....some impressions of the books implications for a "M3/RTT style" trader point of view would be interesting.

The writing style from what I can see in the "look inside this book" on amazon reminds me of a more polished version of "Traders, Guns & Money: Knowns & Unknowns in the Dazzling World of Derivatives" (which had some amusing stories of quants trying to work with traders!).

I agree....some impressions of the books implications for a "M3/RTT style" trader point of view would be interesting.

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If "trader's point of view" means how IV skew will impact a butterfly trade, I don't think this book is meant for that, at least not in a direct manner. This book looks at the IV skew from a modeling perspective and provides some theoretical explanations. In order to digest the book, some level of options math and prior understanding of options modeling is required. I'm still in the early chapters and it'll likely take me a while to finish the book.

Also I'm mostly concerned with the center and right strikes of the BWB, for which SABR produced a reasonably good fit, and ignored the 5 delta puts and calls at the moment

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Nam, after our posts on this I happened to be reading a presentation on VIX options and for some reason one slide had a bunch of SABRE fits to some SPX skews back in 2008 ... they looked interesting enough to me so that I coded up the SABRE thing and tested its fit against some current skews ... what I found is that in order to capture the degree of concavity near the money in, say, the current Dec SPX skew you would need some modification to the standard zero-order SABRE functional form, if not an additional degree of freedom. Specifically, you can get quite a bit of concavity by setting rho VERY close to 1.0, but not quite enough for the examples I tested ... so for some skews you no doubt could fit the butterfly zone, but only by taking something like rho = 0.99999 ... obviously not a stable situation, so my conclusion was that SABRE seems to be a dubious choice for real-life skew modeling, although it might possibly be useful with modifications.

The reason I'm posting is twofold:

If I'm basically right, then I'm giving you the heads up ...

If I'm wrong, for example if a higher-order SABRE function has more flexibility with respect to concavity, or if I just coded the darn thing wrong, then I would appreciate it if you would give me an example of a SABRE fit to a recent SPX skew that doesn't require extreme parameter values ...

I'm guessing the main reason you are getting deafening silence here is because equity index option traders basically have little use for advanced models, the reason being because we don't trade OTC or exotics and the information we need - basically the implied volatility surface - is so dense and rich and updates in real time.

It still seems to be true (at least every time I check, and I just did a check using the Derman book), that stochastic and stochastic+jumps models haven't gone much of anywhere in the last 10 years ... they are great for gathering qualitative insights, but using them for real risk management of exchange-traded portfolios is a non-starter.

My main application of advanced models is to identify functional forms that arise from the models that might be useful, with modifications, to smoothly parameterize the actual skews. In my experience none of them are useful without significant modification, so I'm not using the models directly. The stochastic+jumps models, including the SVJ, all seem to have the disadvantage that there are no closed-form solutions to the skew functions - you need to do numerical integrals. I have no problem doing numerical integrals when it's necessary, but I'm not going to use anything like that as a skew parameterization function unless someone convinces me it is a huge advance over what I've already got.

If "trader's point of view" means how IV skew will impact a butterfly trade, I don't think this book is meant for that, at least not in a direct manner. This book looks at the IV skew from a modeling perspective and provides some theoretical explanations. In order to digest the book, some level of options math and prior understanding of options modeling is required. I'm still in the early chapters and it'll likely take me a while to finish the book.

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Kevin's comment provides exactly the right first paragraph here ... suffice it to say that for every 10 CD members who are convinced to buy this book, 8 of them will be really irritated they fell for it, 1 will be glad they have the book but will never read it, and 1 will actually get something out if it.

I kind of hated this book because it just told me what I already know, but that in itself was valuable to me because it says that as of now I'm probably not missing anything that is generally available to the public (I definitely don't try to keep up to date on this stuff).

But for most folks satisfying Kevin's suggested prerequisites this could be a very good read as the format is solidly pedagogical, in the form of "present simplified model, give a simple example, discuss". The book seems to be intended as an introductory textbook for an advanced undergraduate or first-year graduate finance course.

Chapters 1-7 include a bunch of "cool little things" that are fun and informative to read if you haven't already seen them 10 times.

Chapters 8-13 begin to tackle the skew and includes a very good introduction to the skew-implied distribution.

Chapters 14-17 give an accessible introduction to local volatility models which is pretty much what CD members are using implicitly (yes local volatility is much more than the implied vol surface we use, but for traders who only trade standard expirations in liquid contracts they are arguably equivalent in the practical sense).

Chapters 18-24 on stochastic volatility models is the weakest part of the book in my opinion, which isn't surprising since Derman the local volatility guy stands somewhat in opposition to the stochastic volatility crowd. The problem is that the models and examples are drastically simplified to the point of irritation. Better to skim these chapters quickly and invest your time in a book like Gatheral's "The Volatility Surface".

In summary, you all stand warned by Kevin and then by me: If you buy this book and deeply regret it then I'll give you one clean shot at me, face or body but no below the belt, and beyond that you can only blame yourself.

I had a brief encounter with Professor Derman at Columbia University once - I just happened to walk by him on campus midday. He seemed like a nice guy, and I would've loved to have talked with him about trading, but I didn't want to occupy his time beyond a minute or two.

I've been considering reading his new book because I do love theory; but at this point, I'm more interested in actionable knowledge. Kevin, would you say the book offers any practical applications to the retail trader? Also, have you read his autobiography, 'My Life As a Quant: Reflections on Physics and Finance'? I read most of it, and thought it was a really interesting read. One practical takeaway for me was the realization that for the strategies I trade, the BSM model is sufficient. More to the point, I don't need the perfect model, if one even exists. It's enough to work with the dynamics of 'how wrong' the BSM model is. Complex models do, however, seem to play a much more important role in the pricing of other types of options such as exotics.

Kevin, would you say the book offers any practical applications to the retail trader? Also, have you read his autobiography, 'My Life As a Quant: Reflections on Physics and Finance'? I read most of it, and thought it was a really interesting read. One practical takeaway for me was the realization that for the strategies I trade, the BSM model is sufficient. More to the point, I don't need the perfect model, if one even exists. It's enough to work with the dynamics of 'how wrong' the BSM model is. Complex models do, however, seem to play a much more important role in the pricing of other types of options such as exotics.

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Hi Ice101781

I would say that if one is looking for practical applications, then this is not the right book to read. Most options traders don't understand the BSM formula anyway. There is no need to understand BSM in order to trade.

Having said that, however, it is my belief that in order to truly master anything in life, one would have to learn from first principles, and options modeling is part of the first principles for options trading. Therefore, while there is no immediate practical need to understanding BSM and IV skew in detail in order to trade successfully, having that knowledge will payoff in the future when you want to take your game to the next level (for example - if you want to transition to algorithmic trading or build an expert system using machine learning).

Yes - I have read 'My Life As a Quant'. I like Derman's work. I try to read all his books, articles and listen to his lectures as much as I can.

I'm inclined to agree with this given my experience - it's one thing to understand the derivation of the differential equation that underpins the BSM model, but it's quite another to understand the solution to that differential equation which actually yields the formulas for European-style calls and puts. Hopefully, a clearer understanding of the foundations provides another bit of edge in practice in much the same way it does for other disciplines.

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